Let f: (- 1, 1) → R be a function defined by f(x) = max\ - |x|, - 1 - x ^ 2 \ . If K be the set of all points at which f is not differentiable, then K has exactly

Correct answer: C. three elements From the graph, it can be concluded that f (x) is non-differentiable at x = 0, ± 1 2 in (- 1, 1) . ∴ At 3 points in (- 1, 1).

JEE Main 201910 JanuaryEvening Shift

Exam: JEE Main
Year: 2019
Date: 10 January
Shift: Evening Shift
Subject: Mathematics
Chapter: Continuity and Differentiability

JEE Main 2019 · 10 January · Evening Shift · Mathematics · Continuity and Differentiability

Let f: (- 1, 1) → R be a function defined by f(x) = max\ - |x|, - 1...

Let

f: \left(- 1, 1\right) \to R

be a function defined by

f\left(x\right) = max\left\{- \left|x\right|, - \sqrt{1 - {x}^{2}}\right\} .

K

be the set of all points at which

f

is not differentiable, then

K

has exactly $Let f: (- 1, 1) → R be a function defined by f(x) = max\ - |x|, - 1 - x ^ 2 \ . If K be the set of all points at which$

Options

Atwo elements
Bone element
Cthree elements
Dfive elements

Correct answer

C. three elements

Step-by-step solution

$Let f: (- 1, 1) → R be a function defined by f(x) = max\ - |x|, - 1 - x ^ 2 \ . If K be the set of all points at which$

From the graph, it can be concluded that $f$ \left(x\right) $is non-differentiable at$ x = 0, \pm \dfrac{1}{\sqrt{2}} $in \left(- 1, 1\right)$ .

$∴$ At $3$ points in \left(- 1, 1\right).

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